Question: Simplify the following expression: $ q = \dfrac{-9}{10} - \dfrac{z - 3}{9z} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9z}{9z}$ $ \dfrac{-9}{10} \times \dfrac{9z}{9z} = \dfrac{-81z}{90z} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{z - 3}{9z} \times \dfrac{10}{10} = \dfrac{10z - 30}{90z} $ Therefore $ q = \dfrac{-81z}{90z} - \dfrac{10z - 30}{90z} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-81z - (10z - 30) }{90z} $ Distribute the negative sign: $q = \dfrac{-81z - 10z + 30}{90z}$ $q = \dfrac{-91z + 30}{90z}$